PRP Records

Probable Primes Top 10000

(277054 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 50000) Who ? When ?
800144^49524+4381391Norbert Schneider06/2014
8002(3*2^270368-1)/1381389Lelio R Paula02/2014
800319548^14563+14563^1954881384Hans Havermann05/2020
8004(2^270337+1130)/281380Stefano Morozzi01/2020
800527405^932+932^2740581377Hans Havermann05/2020
800619396^15683+15683^1939681375Hans Havermann05/2020
8008(10^81363+719)/981363Serge Batalov12/2014
8007(734^28393-1)/73381363Serge Batalov08/2020
8009(10^81353+449)/981353Serge Batalov12/2014
801014^70978-8981350Lelio R Paula11/2015
801111^78108-204081342Enzo Doria12/2012
80127*10^81327-5781328Robert Price06/2020
8013(7*10^81328-79)/981328Robert Price01/2021
801419102^18065+18065^1910281315Hans Havermann07/2020
80153^170400-5881302Lelio R Paula12/2015
8016(17*10^81300-131)/381301Robert Price12/2017
801710^81297+3699181298Patrick De Geest06/2013
801810^81297-5781297Robert Price05/2011
8019(2^270063+3206)/281297Stefano Morozzi01/2020
802019359^15826+15826^1935981296Hans Havermann06/2020
80212^270055-11304781295Enzo Doria07/2014
802218^64759-5581291Lelio R Paula11/2015
8023(2^269987+1)/381274H.&R. Lifchitz10/2000
8024(31^54493-1)/3081268Alexander Zhirkov10/2010
8025(2^270059-1)/540119/6481417/712497615775672596781265Dario Alpern09/2014
8026(194^35521-1)/19381263Serge Batalov08/2020
802720722^8343+8343^2072281258Hans Havermann07/2020
8028(2^269922+3574)/281255Stefano Morozzi01/2020
802921310^6497+6497^2131081249Hans Havermann07/2020
8030(16392^19273-1)/1639181225Serge Batalov08/2020
80312^269819-459781224Yves Minet03/2019
8032(2^269816+7)/42490181218Lelio R Paula12/2012
803323470^2887+2887^2347081217Hans Havermann05/2020
8034(23*10^81214+1)/381215Serge Batalov06/2009
8035(2^269720+3778)/281194Stefano Morozzi01/2020
8036(17*2^269720+1)/30381193Lelio R Paula07/2012
803756^46441-55^4644181188Robert Price10/2013
80382^269664+17781177Lelio R Paula06/2012
8039(13*2^269665-1)/18581177Lelio R Paula02/2014
804021642^5615+5615^2164281144Hans Havermann07/2020
80412^269539-11224981140Enzo Doria06/2014
8042((2*170026-3)*3^(170026-1)+1)/481128Robert Price01/2015
8044(2^269495-5)/981126Lelio R Paula12/2012
80431239^26228+26228^123981126Norbert Schneider10/2019
80452^269490-362381125Yves Minet10/2009
8046(55459*2^269444+1)/3581114Lelio R Paula06/2014
804719554^14065+14065^1955481113Hans Havermann06/2020
8048(2^269417+78557)/525781099Lelio R Paula12/2012
80494*5^116011-781089Lelio R Paula10/2014
8050(2^269349+2366)/281082Stefano Morozzi01/2020
8051(2^269303+2946)/281068Stefano Morozzi01/2020
80526*10^81060+5381061Robert Price05/2020
80537*10^81058+7981059Robert Price02/2017
80542^269236-10990781049Enzo Doria04/2014
8055(2^269182+1870)/281032Stefano Morozzi01/2020
8056(2^269179+3006)/281031Stefano Morozzi01/2020
8057(8*10^81029-11)/381030Erik Branger03/2014
805819749^12668+12668^1974981025Hans Havermann05/2020
80593*10^81021+781022Erik Branger11/2013
80606^104115+10381018Lelio R Paula12/2015
80612^269120+186915181014Enzo Doria05/2016
80625^115901+1281012Lelio R Paula10/2015
8063(2^269072+3610)/280999Stefano Morozzi01/2020
8064(2^269083-9)/32036980997Lelio R Paula12/2012
8065(5*10^80992-179)/380993Robert Price10/2020
80662*10^80981-4980982Robert Price09/2020
8067(2^269002+1614)/280978Stefano Morozzi01/2020
806817^65810-2080976Lelio R Paula11/2015
806920^62236-2380971Lelio R Paula01/2016
80702^268974-11218180970Enzo Doria06/2014
8072L(387433)80969Renaud Lifchitz11/2003
8071V(387433)80969Serge Batalov03/2015
807322732^3645+3645^2273280965Hans Havermann06/2020
8074(2^268957+602)/280964Stefano Morozzi01/2020
8075(2^268955-509203)/580963Lelio R Paula12/2012
807619485^14284+14284^1948580958Hans Havermann05/2020
8077(87398^16384+1)/6553780957Lelio R Paula11/2011
8078329^32160+32160^32980954Norbert Schneider11/2014
807919678^12973+12973^1967880937Hans Havermann02/2020
8080(2^268864+3558)/280936Stefano Morozzi01/2020
80812^268859-15980935Lelio R Paula05/2012
8082(2^268841-lucasV(1,2,268841)+1)/280929Mike Oakes11/2016
80842^268827+577580925Lelio R Paula07/2013
80832^268824-11025580925Enzo Doria05/2014
8085(2^268824+1902)/280924Stefano Morozzi01/2020
80862^268798-186832180917Enzo Doria04/2016
808720613^8420+8420^2061380913Hans Havermann03/2020
80882^268753-11462180903Enzo Doria05/2015
80892^268743+160580900Lelio R Paula07/2013
80906^103954-13980892Lelio R Paula12/2015
809110^80883+4980884Robert Price03/2011
809210^80883-8032780883Patrick De Geest07/2013
80936^103937+12180879Lelio R Paula12/2015
8094148^37266+14780877Norbert Schneider12/2018
8095(26*10^80875-119)/380876Robert Price07/2016
8096(22699*2^268657+1)/635180875Lelio R Paula06/2014
8097(2^268612+2530)/280860Stefano Morozzi01/2020
80982^268581-86968810580851Lelio R Paula05/2016
8099(11*2^268521-1)/380834Lelio R Paula02/2014
81002^268516-24980832Yves Minet02/2012
810122259^4278+4278^2225980828Hans Havermann03/2020
81022^268500+1609580827Lelio R Paula07/2013
81033^169402+10080826Lelio R Paula12/2015
8104(2^268495+566)/280825Stefano Morozzi01/2020
81059^84698+8^(84698-1)80823Robert Price03/2016
81062^268472-10973980819Enzo Doria04/2014
8107(9*2^268454+1)/3780813Lelio R Paula12/2012
8108(3*2^268502+1)/37790218843535364780811Lelio R Paula12/2012
8109(2^268441+3962)/280809Stefano Morozzi01/2020
8110134^37987-133^3798780803Jean-Louis Charton12/2005
811115^68702-7680800Lelio R Paula11/2015
81122^268408+780799Lelio R Paula05/2012
8113(16095^19207-1)/1609480794Serge Batalov08/2020
81142^268375+14180789Lelio R Paula05/2012
811512^74856-4780784Lelio R Paula11/2015
81162^268346+52428780781Paul Underwood08/2018
81179*10^80777-4180778Robert Price08/2020
8118(10868^20011-1)/1086780764Serge Batalov08/2020
81196^103770-10780749Lelio R Paula12/2015
8120(751^28081-1)/75080748Serge Batalov08/2020
81213^169224-6280741Lelio R Paula12/2015
8122p(16866)#/2+6480741Robert Price03/2017
81235^115502-7280733Lelio R Paula10/2015
8124(2^268154+2262)/280723Stefano Morozzi01/2020
8125(2^268156+1290)/280723Stefano Morozzi01/2020
81272^268079-192780700Yves Minet10/2009
8126(2^268078+2514)/280700Stefano Morozzi01/2020
81282^268028+11780685Lelio R Paula05/2012
8129121^38738+12080683Norbert Schneider01/2015
8130(3^169097-8)/83580677Lelio R Paula12/2012
8131(2^267956+1810)/280663Stefano Morozzi01/2020
813219359^14666+14666^1935980656Hans Havermann12/2019
81332^267918+6780652Lelio R Paula05/2012
8134(89*10^80650-179)/980651Robert Price11/2017
8135(2^267914+2094)/280650Stefano Morozzi01/2020
8136(2^267894+2202)/280644Stefano Morozzi01/2020
8137(302*10^80638+13)/980640Robert Price01/2017
81383^169004+266080636Lelio R Paula12/2015
81392^267860-11285980634Enzo Doria06/2014
81402^267828-11070580625Enzo Doria05/2014
8141(2956^23227-1)/295580611Serge Batalov08/2020
8142(2^267752+2602)/280602Stefano Morozzi01/2020
81432^267743+1270580599Lelio R Paula07/2013
8144(22*10^80595+23)/980596Robert Price03/2015
8145(2^267712+2358)/280590Stefano Morozzi01/2020
8146(2^267685+854)/280581Stefano Morozzi01/2020
81472^267674-5180578Lelio R Paula05/2012
8148(86*10^80571-41)/980572Robert Price11/2015
8149(2^267637+2454)/280567Stefano Morozzi01/2020
815020452^8693+8693^2045280564Hans Havermann02/2020
81512^267612-196580560Lelio R Paula07/2013
81522^267553+409780542Lelio R Paula07/2013
81537^95276-880518Robert Price01/2014
8154(15185*2^267457-1)/4782980513Lelio R Paula04/2015
81556^103467+16380513Lelio R Paula12/2015
815620283^9314+9314^2028380506Hans Havermann02/2020
8157(2^267387+2294)/280492Stefano Morozzi01/2020
8158(7*10^80490+143)/380491Robert Price04/2016
815919887^11152+11152^1988780490Hans Havermann01/2020
8160(2^267348+3810)/280480Stefano Morozzi01/2020
816186^41597-85^4159780470Robert Price04/2015
816213^72237+3080468Lelio R Paula11/2015
816317^65389+1480458Lelio R Paula11/2015
8164423^30634+30634^42380456Norbert Schneider05/2017
8165(2^267257+470)/280453Stefano Morozzi01/2020
81662^267232+10580445Lelio R Paula05/2012
8167(298*10^80442+11)/380444Robert Price11/2020
816822101^4360+4360^2210180437Hans Havermann02/2020
816911^77237-307200080435Enzo Doria01/2013
817020696^7689+7689^2069680422Hans Havermann01/2020
8171(2^267149+2562)/280420Stefano Morozzi01/2020
817221321^5908+5908^2132180411Hans Havermann02/2020
8173(13100^19531-1)/1309980411Serge Batalov08/2020
81742^267116-45995980410Enzo Doria06/2015
817538715!2+880406Robert Price01/2015
817619579^12786+12786^1957980406Hans Havermann02/2020
8177(2^267017+1)/380380H.&R. Lifchitz09/2000
8178(2^267006+1134)/280377Stefano Morozzi01/2020
817924273^2048+2048^2427380376Hans Havermann01/2020
8180(2^266989+734)/280372Stefano Morozzi01/2020
8181(2^266989+1850)/280372Stefano Morozzi01/2020
8182(13427^19471-1)/1342680372Serge Batalov08/2020
81832^266968-4580366Lelio R Paula05/2012
8184(2^266967+3974)/280365Stefano Morozzi01/2020
818520^61768-6380363Lelio R Paula01/2016
8186(6253^21169-1)/625280356Serge Batalov08/2020
8187(14005^19381-1)/1400480355Serge Batalov08/2020
81882^266920-11296780351Enzo Doria06/2014
8189(2^266910+2394)/280348Stefano Morozzi01/2020
8190(2^266899+1994)/280345Stefano Morozzi01/2020
81918*10^80342+8780343Robert Price10/2017
8192(10^80363+1)/1186613600417422195087690646380335Anonymous10/2020
8193(2^266861+890)/280333Stefano Morozzi01/2020
819412^74428-1380322Lelio R Paula11/2015
8195(2^266810+2718)/280318Stefano Morozzi01/2020
8196(2^266800+2886)/280315Stefano Morozzi01/2020
8197(6163^21187-1)/616280291Serge Batalov08/2020
81982^266680+2780279Lelio R Paula05/2012
81992^266630-13180264Lelio R Paula05/2012
8200(2^266627+1278)/280263Stefano Morozzi01/2020
82012^266598+7681980254Enzo Doria05/2016
820224463^1908+1908^2446380253Hans Havermann01/2020
82032^266587+188063380251Enzo Doria10/2016
8204(2^266570+3942)/280246Stefano Morozzi01/2020
82052^266541-11004980237Enzo Doria04/2014
820638635!2-880222Robert Price06/2015
8207(2^266465+986)/280214Stefano Morozzi01/2020
82083^168111+168111^3-180210Robert Price04/2014
8209(2^266447+758)/280209Stefano Morozzi01/2020
82102^266443+51380208Lelio R Paula07/2013
8211(26*10^80200+61)/380201Robert Price06/2017
82122^266412-10991380199Enzo Doria04/2014
8213(10223*2^266417+1)/4509180199Lelio R Paula06/2014
82142^266413-469380199Yves Minet05/2019
8215(13737^19381-1)/1373680193Serge Batalov08/2020
821613^71988+6680191Lelio R Paula11/2015
821711^77002-432080190Enzo Doria01/2013
821819839^11012+11012^1983980187Hans Havermann03/2020
822018^63879-1380186Lelio R Paula11/2015
8219(2^266371+1814)/280186Stefano Morozzi01/2020
82212^266368-11229580185Enzo Doria06/2014
822219217^14880+14880^1921780185Hans Havermann03/2020
8223(3^168050+5)/102145480175Lelio R Paula10/2012
8224(2^266324+1386)/280172Stefano Morozzi01/2020
8225(22*10^80167+41)/980168Robert Price02/2015
8226(2^266308+1618)/280167Stefano Morozzi01/2020
8227(34*10^80162-43)/980163Ray Chandler12/2010
8228(2^266276+762)/280157Stefano Morozzi01/2020
8230(38*10^80150-11)/980151Robert Price05/2015
8229(598*10^80149-31)/980151Robert Price02/2017
823119^62678-8080150Lelio R Paula12/2015
8232(559^29173-1)/55880148Serge Batalov08/2020
823310^80139+3234380140Patrick De Geest02/2011
823410^80139-980139Alexander Gramolin01/2011
82353^167955-10680135Lelio R Paula12/2015
823620545^7944+7944^2054580127Hans Havermann04/2020
823718876^17569+17569^1887680124Hans Havermann03/2020
8238(2^266137+3782)/280115Stefano Morozzi01/2020
8239(2^266121+3846)/280111Stefano Morozzi01/2020
824022752^3313+3313^2275280093Hans Havermann03/2020
8241(197*10^80089-11)/380091Robert Price10/2017
82422^265998+7555980074Enzo Doria04/2016
8243(2^265999+3290)/280074Stefano Morozzi01/2020
82442^265969-10980180065Enzo Doria04/2014
8245(2^265956+3378)/280061Stefano Morozzi01/2020
8246(185*10^80051-11)/380053Robert Price10/2020
82472^265888-11275780041Enzo Doria06/2014
8248(24847^18211-1)/2484680038Serge Batalov08/2020
82492^265809+170180017Lelio R Paula07/2013
8250gcd(V(957175),5*F(191435)*(F(191435)+1)+1)80014Serge Batalov04/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 25 2021 11:23 (Time in France)

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